NEW YORK (CBS News/CBS SF) — New York real estate heir Robert Durst was sentenced Thursday to life in prison without chance of parole for the murder of his best friend and former KPIX producer Susan Berman more that two decades ago.

Durst, 78, was convicted in Los Angeles Superior Court last month of first-degree murder for shooting Berman point-blank in the back of the head at her home in December 2000. Durst silenced Berman to prevent her from incriminating him in the reopened investigation of his wife’s 1982 disappearance in New York, prosecutors said.

READ MORE: 'It’s A Big One'; Weekend Atmospheric River Gaining Intensity Off California Coast

Berman had also provided a phony alibi for Durst when Kathie Durst vanished, according to prosecutors.

ALSO READ: Eccentric Millionaire Arrested On Murder Warrant Linked To Former KPIX Producer’s Death

Durst had always maintained his innocence in the 2000 murder of Berman, whose father was an associate of Las Vegas mobsters Bugsy Siegel and Meyer Lansky.

The then 55-year-old Berman was a writer who became Durst’s spokeswoman. She was killed at her home near Beverly Hills with a bullet to the back of her head as New York investigators prepared to question her in the unsolved 1982 disappearance of Durst’s wife, Kathleen.

Berman had worked as a writer and producer for KPIX 5’s Evening Magazine when the show first launched in the 1970’s. She was also a writer for the Examiner.

“The jig is up,” said former Westchester County District Attorney Jeanine Pirro, who had hoped Berman would help solve the disappearance.

Durst, a wealthy eccentric linked to two killings and his wife’s disappearance, came on Sunday just before the finale in an HBO show about his life in which he said he “killed them all.”

Durst was arrested on a murder warrant in New Orleans in 2015, just prior to the airing of the finale of an HBO serial documentary about his links to three sensational killings.

READ MORE: White House Unveils COVID Vaccination Plans For Children Age 5-11

In the finale, Durst was asked about similarities in handwriting in a letter he wrote and another linked to one of the killings. Later, filmmakers said Durst wore his microphone into the bathroom.

What followed was a bizarre rambling in which Durst said, apparently to himself, “There it is. You’re caught” and “What the hell did I do? Killed them all of course.”

The show ended, and it wasn’t clear whether producers confronted Durst about the secretly recorded words, or what Durst meant by them.

Durst participated in the HBO documentary, giving an extensive interview to filmmaker Andrew Jarecki for “The Jinx: The Life and Deaths of Robert Durst.”

The documentary series revealed a hand-written address on a letter, recovered by the slain woman’s relative, that Durst had sent to Berman. The handwriting seems virtually identical to an anonymous letter alerting Beverly Hills police to a “cadaver” in Berman’s home. Even the word “Beverly” is misspelled as “Beverley” on both documents.

Durst observes in the documentary that only Berman’s killer could have sent the letter to police.

Jarecki is then shown putting the other letter in a safe deposit box.

The documentary didn’t indicate whether Jarecki shared that earlier letter with the authorities, but in 2015, the Los Angeles Police said the arrest resulted from “investigative leads and additional evidence that has come to light in the last year.”

At the time of his arrest in 2015, Durst’s estranged and fearful relatives thanked authorities for tracking him down.

MORE NEWS: Suspect In Shopping Center Parking Lot Shootout With Milpitas Police Dies Of Wounds

“We are relieved and also grateful to everyone who assisted in the arrest of Robert Durst.  We hope he will finally be held accountable for all he has done,” said his brother, Douglas Durst, in a statement.